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The standard gravitational parameter μ of a celestial body is the product of the gravitational constant G and the mass M of that body. For two bodies, the parameter may be expressed as G ( m 1 + m 2 ) , or as GM when one body is much larger than the other: μ = G ( M + m ) ≈ G M . {\displaystyle \mu =G(M+m)\approx GM.}
Earth's gravity measured by NASA GRACE mission, showing deviations from the theoretical gravity of an idealized, smooth Earth, the so-called Earth ellipsoid.Red shows the areas where gravity is stronger than the smooth, standard value, and blue reveals areas where gravity is weaker (Animated version).
The standard acceleration of gravity or standard acceleration of free fall, often called simply standard gravity and denoted by ɡ 0 or ɡ n, is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. It is a constant defined by standard as 9.806 65 m/s 2 (about 32.174 05 ft/s 2).
The quantity GM —the product of the gravitational constant and the mass of a given astronomical body such as the Sun or Earth—is known as the standard gravitational parameter (also denoted μ). The standard gravitational parameter GM appears as above in Newton's law of universal gravitation, as well as in formulas for the deflection of ...
Its geometric parameters are: semi-major axis a = 6378137.0 m, and flattening f = 1/298.257222101. If we also require that the enclosed mass M is equal to the known mass of the Earth (including atmosphere), as involved in the standard gravitational parameter, GM = 3986005 × 10 8 m 3 ·s −2, we obtain for the potential at the reference ellipsoid:
Every object in a 2-body ballistic trajectory has a constant specific orbital energy equal to the sum of its specific kinetic and specific potential energy: = = =, where = is the standard gravitational parameter of the massive body with mass , and is the radial distance from its center. As an object in an escape trajectory moves outward, its ...
The "mass of the earth in gravitational measure" is stated as "9.81996×6370980 2" in The New Volumes of the Encyclopaedia Britannica (Vol. 25, 1902) with a "logarithm of earth's mass" given as "14.600522" [3.985 86 × 10 14]. This is the gravitational parameter in m 3 ·s −2 (modern value 3.986 00 × 10 14) and not the absolute mass.
At a fixed point on the surface, the magnitude of Earth's gravity results from combined effect of gravitation and the centrifugal force from Earth's rotation. [2] [3] At different points on Earth's surface, the free fall acceleration ranges from 9.764 to 9.834 m/s 2 (32.03 to 32.26 ft/s 2), [4] depending on altitude, latitude, and longitude.